Observer based adaptive robust control of a class of nonlinear systems with dynamic uncertainties

The discontinuous projection based adaptive robust control (ARC) scheme is generalized to a class of nonlinear systems in an extended semi-strict feedback form by incorporating a nonlinear observer and a dynamic normalization signal. The unmeasured states associated with the dynamic uncertainties are assumed to enter the system equations in an affine fashion. A novel nonlinear observer is first constructed to estimate the unmeasured states for a less conservative design. Estimation errors of dynamic uncertainties, as well as other model uncertainties, are dealt with effectively via certain robust feedback control terms for a guaranteed robust performance. In contrast with existing conservative robust adaptive control schemes, the proposed ARC method makes full use of the available structural information on the unmeasured state dynamics and the prior knowledge on the bounds of parameter variations for high performance. The resulting ARC controller achieves a prescribed transient performance and final tracking accuracy in the sense that the upper bound on the absolute value of the tracking error over entire time-history is given and related to certain controller design parameters in a known form. Furthermore, in the absence of uncertain nonlinearities, asymptotic tracking is also achieved.